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Determine whether a comparable rigorous bound on $T_c$ exists in three dimensions, and in flat-band systems where the superfluid stiffness has a quantum-geometric contribution. An answer is a proof with stated assumptions or a counterexample model.","problem_ref":null,"references":"","settled_by":"A proof bounding $T_{c}$ by stiffness or kinetic-energy sum rules in 3D, or a solvable 3D model violating any such bound.","status_note":"","title":"Do superfluid-stiffness bounds on $T_c$ extend to three 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